Is the Ecliptic Plane the Same as the Apparent Path of the Sun?

[KurtLudwig]

TL;DR Summary

Does beta, the angle to the ecliptic plane, of distant stars change? If it does it is probably very little over a long period of time.

Please correct my statements: By definition, the ecliptic plane is the path of the Earth around our Sun. Beta of Earth is 0.0000.
The ecliptic is very flat since Jupiter is only 0.5 degrees off the ecliptic.
From Wikipedia: " The ecliptic is actually the apparent path of the Sun throughout the course of a year." Is that the same as the ecliptic plane is the path of the Earth around our Sun?

 

[snorkack]

It does. Like:
https://ufdc.ufl.edu/AA00002116/00001/1j

 

[Bandersnatch]

From Wikipedia: " The ecliptic is actually the apparent path of the Sun throughout the course of a year." Is that the same as the ecliptic plane is the path of the Earth around our Sun?

Yes. It's just a matter of choosing your reference frame - from the Sun it appears that the Earth is moving, from Earth it's the Sun. But it's the same motion, in the same plane.